In control units used in motor vehicles, properties of subsystems must be simulated to determine state variables which are important for regulators, for example, and are not directly measurable or are not measured for cost reasons online.
Two different approaches are known for modeling in control units. In the first approach, relevant technical physical system properties are simulated by a mathematical model, such as a differential equation system. The second possibility is by explicit storage of the system information of interest as a function of relevant influencing parameters in an engine characteristics map. Relationships among a plurality of influencing parameters are represented in such an engine characteristics map.
For use in a motor vehicle in particular, the characteristics map representation has advantages in terms of both the demand on computation time as well as simplification of the calibration. This is due to the fact that a complex model computation is not necessary, and instead the desired values are obtained directly from the engine characteristics map.
The use of engine characteristics maps is described in German Patent Application No. DE 198 03 853, for example, which describes a method and a device for regulating the intake air temperature of an internal combustion engine. The device described therein ensures that a cooling device is turned on and off so as to achieve optimum engine efficiency. This assumes that the firing angle efficiency is an indicator of the knocking tendency of the engine and that the firing angle efficiency is determined as a function of the engine speed and the engine load to adjust an optimum setpoint torque of the engine by varying the filling and the firing angle setting.
It is often necessary to analyze engine characteristics map data in two directions. This means that an inversion of the engine characteristics map is necessary in analysis of a first engine characteristics map
KF1: x3=f(x1, x2)
and a second engine characteristics map
KF2: x2=f(x1, x3).
Thus, the desired engine characteristics map
x2=f(x1, x3)
is generated from the given database
x3=f(x1, x2)
by interpolation on the basis of predetermined interpolation points x3i.
Interpolation points are predetermined value pairs which are determined empirically or by computation and therefore constitute the basic grid in the engine characteristics map.
However, one disadvantage of the conventional engine characteristics map inversion is that when both conversions must be performed directly in succession one after the other in one step of the computation grid, namely
X30′=f(x10, x20), x20′=f(x10, x30′),
consistency cannot be ensured under all boundary conditions, i.e., x20 is not identical to x20′.
The reason for this lies in the generation of a fixed interpolation point grid in generating the second engine characteristics map from the first engine characteristics map. Depending on the position of x20 and the interpolation point grid, x30′ in the reverse calculation is situated in an interpolation field defined by the interpolation points of the second engine characteristics map, which were used as interpolation points for the interpolation on other interpolation points of the starting database of the first engine characteristics map. Consequently, in analysis of the second engine characteristics map, different interpolation points have an influence on the x20′ result than in analysis of the first engine characteristics map for the x30′ result.